<p><b>Abstract</b>—For large time-varying data sets, memory and disk limitations can lower the performace of visualization applications. Algorithms and data structures must be explicitly designed to handle these data sets in order to achieve more interactive rates. The Temporal Branch-on-Need Octree (T-BON) extends the three-dimensional branch-on-need octree for time-varying isosurface extraction. This data structure minimizes the impact of the I/O bottleneck by reading from disk only those portions of the search structure and data necessary to construct the current isosurface. By performing a minimum of I/O and exploiting the hierarchical memory found in modern CPUs, the T-BON algorithm achieves high performance isosurface extraction in time-varying fields. This paper extends earlier work on the T-BON data structure by including techniques for better memory utilization, out-of-core isosurface extraction, and support for nonrectilinear grids. Results from testing the T-BON algorithm on large data sets show that its performance is similar to that of the three-dimensional branch-on-need octree for static data sets while providing substantial advantages for time-varying fields.</p>